The PageRank vector
The Ranking of Nodes in Networks

As we have seen, according to the Perron-Frobenius theorem, r_c ≥ 0. We normalize this vector so that e^Tr_c = 1; it is, therefore, a probability vector.

We will express r_c in different ways: implicit, explicit and polynomial expressions of the PageRank vector.

Note that from the iterates of the power method, it is possible to obtain rational and polynomial approximations of the vector r_c. These approximations are based on the corresponding exact expressions given below, simply by choosing smaller degrees. In particular, Padé-type approximations can be constructed. On these issues, the reader can consult